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The paper has two main parts: First we make the connection between monotone modal logic and the general theory of coalgebras precise by defining functors UpP : Set → Set and UpV : Stone → Stone such that UpPand UpV-coalgebras correspond to monotone neighbourhood frames and descriptive general monotone frames, respectively. Then we investigate the relationship between the coalgebraic notions of equivalence and monotone bisimulation. In particular, we show that the UpP-functor does not preservedoi:10.1016/j.entcs.2004.02.028 fatcat:sobmaoiz4renfnbkip6mii4vja